Transcript GIS and Remote Sensing in Water Resources Management

Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Digital Terrain Mapping and
Analysis
Dr. A.K.M. Saiful Islam
Institute of Water and Flood Management (IWFM)
Bangladesh University of Engineering and Technology (BUET)
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Lecture Topic
This lecture will focus on
• Geo-referencing
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Coordinate Systems
Map Projections
Coordinate Transform
Map & Time Distance, Scale and accuracy
Interpolation techniques
• Digital Terrain Mapping and Analysis
– DEM
– DTM
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Coordinate Systems
Geospatial data should be geographically referenced ( called
georeferenced or geocoded) in a common coordinate system.
 Plane Orthogonal Coordinates
One of the most convenient way of locating points is to use
plane orthogonal coordinates with x (horizontal) and y (vertical)
axis.
 Polar Coordinates
A polar coordinate system with the angle (q ) measured from
the polar axis (x axis) and distance (r) from the pole is used in
some cases.
 3D Orthogonal Coordinates
Three dimensional (3D) orthogonal coordinates are also used
to locate points with the plane coordinates (x, y) and height or
depth (z).
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Plane Orthogonal Cartesian
Coordinates
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Polar coordinates
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
3D Coordinate System
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
The Shape of the Earth
• The shape of the Earth can be represented by an ellipsoid of
rotation (or called a spheroid) with the lengths of the major semiaxis (a) and the minor semi-axis (b).
• Two type of coordinate system use: (i) Geodetic, (ii) Geocentric
coordinates
Geodetic and Geocentric Latitude
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
 

Geocentric Latitude – The acute angle measured perpendicular to
the equatorial plane and a line joining the center of the earth and a
point on the surface of the reference ellipsoid.
Geodetic Latitude – The acute angle between the equator and a line
drawn perpendicular to the tangent of the reference ellipsoid. Map
coordinates are given as longitude and geodetic latitude.
[Source : http://ccar.colorado.edu/ASEN5070/handouts/geodeticgeocentric.doc ]
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Map Projection
• A map projection is a process of transforming location on
the curved surface of the Earth with the geodetic
coordinates (j , l) to planar map coordinates (x, y).
• More than 400 difference map projections have been
proposed. The map projections are classified by the
following parameters.
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projection plane: perspective, conical, cylindrical
aspect: normal, transverse, oblique
property: conformality, equivalence, equidistance
size: inside, tangent, secant
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Projection property
1. Conformality is the characteristic of true shape, wherein a projection
preserves the shape of any small geographical area. This is
accomplished by exact transformation of angles around points.
– The property of conformality is important in maps which are used for
analyzing, guiding, or recording motion, as in navigation.
2. Equivalence is the characteristic of equal area. Preservation of
equivalence involves an inexact transformation of angles around
points and thus, is mutually exclusive with conformality except along
one or two selected lines.
– The property of equivalence is important in maps which are used for
comparing density and distribution data, as in populations.
3. Equidistance is the characteristic of true distance measuring. The
scale of distance is constant over the entire map.
– Equidistance is important in maps which are used for analyzing
velocity, e.g. ocean currents. Typically, reference lines such as the
equator or a meridian are chosen to have equidistance and are termed
standard parallels or standard meridians.
[ Source: http://www.forestry.umt.edu/academics/courses/FOR503/Part4.htm ]
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Perspective Projection
• Perspective projections are classified based on the
projection center or viewpoint.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Conical Projection
• Conical projections are classified by the
aspect as well as the cone size
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Conic projection
Conic (tangent)
Conic (secant)
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Cylindrical Projections
• Cylindrical projections are classified as in case of conical
projections. One of the most popular cylindrical projections is the
Universal Transverse Mercator (UTM) with a transverse axis, secant
cylinder and conformality (equal angle).
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
UTM Projection
• Universal Transverse
Mercator (UTM) with a
transverse axis, secant
cylinder and conformality
(equal angle).
• UTM is commonly used for
topographic maps of the
world, devided into 60
zones with a width of 6
degree longitude.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Coordinate Transformation
Coordinate transformation is to transform a
coordinate system (x, y) to another coordinate
system (u, v). The transformation is needed in the
following cases:
– to transform different map projections of many GIS
data sources to an unified map projection in a GIS
database,
– to adjust errors which occur at map digitization
due to shrinkage or distortion of the map
measured, and
– to produce geo-coded image by so called
geometric correction of remote sensing imagery
with geometric errors and distortions.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Reference for Coordinate
Transformation
• Coordinate transformation is executed by a selected
transformation model (or mathematical equation), with
a set of reference points (or control points), that are
selected as tic masks at the corner points, reseau or
ground control points.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Major Transformation
a)
Helmert
Transformation
scale, rotation and shift
b)
Affine Transformation
skew, scale of x and y,and
shift
c)
Pseudo Affine
Transformation
bi-linear distortion
d)
Quadratic
Transformation
parabolic distortion
e)
Perspective Projection
rectification of aerial photo
f)
Cubic Transformation
cubic and distortion)
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Distance
•
Distance is one of the important elements in measuring spatial objects in
GIS. Several different concepts of distance are defined as follows.
•
Euclidean Distance
Euclidean distance D is the defined as the distance measured along a
straight line from point (x1, y1 ) to point (x2, y2 ) in Cartesian coordinate
system . D2 = ( x1 - x2 )2 + ( y1- y2 )2
•
Manhattan Distance
Manhattan distance D is defined as the rectilinear rout measured along
parallels to X and Y axes
D = | x1 - x2| + | y1-y2|
•
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Distances (Contd..)
•
Great Circle Distance
Great circle distance D is defined as
distance along the great circle of the
spherical Earth surface from a point (1,
1; latitude and longitude) to another
point (2, 2) where R is the radius of the
Earth (R = 6370.3 km) on the assumption
that the Earth is a sphere.
•
Mahalanobis Distance
Mahalanobis distance D is a normalized
distance in the normal distribution from
the center (X0) to a point (X) in case of n
dimensional normal distribution.
Mahalanobis distance is used in the
maximum likelihood method for the
classification of multi-spectral satellite
images. where S: variance-covariance
matrix
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Distances (Contd..)
Time Distance
• Time distance is defined as the time required to move from point B
to point A by using specific transportation means.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Scale, Accuracy and Resolution
• Scale of map refers to the ratio of distance on a map over the
corresponding distance on the ground.
• The scale is represented as 1: M or 1/M, where M is called the scale
denominator.
• The larger the scale, the more the detail described by the map and
with higher accuracy.
• Accuracy is generally represented by standard deviation of errors,
that is difference between measurements and the true value.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Relationship between scale,
accuracy and resolution
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Principle of Interpolation
Interpolation is the procedure of estimating
the value of properties at unsampled points or
areas using a limited number of sampled
observations.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Interpolation Techniques
• 1. Pointwise interpolation
• 1(a) Thiessen polygon
• 1(b) Weighted Average
• 2. Interpolation by curve fitting
– 2.1 Exact interpolation
• 2. 1(a). Nearest neighbor
• 2. 1.(b) Linear interpolation
• 2. 1(c) Cubic interpolation
– 2.2 Approximate interpolation
• 2.2(a) Moving Average
• 2.2(b) B-spline
• 2.2(c) Curve Fitting by Least Square Method
 3. Interpolation by surface fitting
– 3.1 Regular grid
• 3.1(a) Bilinear Interpolation
• 3.1(b) Bicubic Interpolation
– 3.2 Random points
• 3.2(a) TIN
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
1. Pointwise Interpolation
 Pointwise interpolation is used in case the sampled
points are not densely located with a limited influence
or continuity in surrounding observations, for example
climate observations such as rainfall and
temperature, or ground water level measurements at
wells.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
1(a) Thiessen Polygons
 Thiessen polygons can be generated using distance
operator which creates the polygon boundaries as the
intersections of radial expansions from the observation
points.
 This method is also known as Voronoi tessellation.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
1(b) Weighted Average
 A window of circular shape with the radius of
dmax is drawn at a point to be interpolated, so
as to involve six to eight surrounding
observed points.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
2. Interpolation by Curve Fitting
 the principle of curve fitting respectively to
interpolate the value at an unsampled point
using surrounding sampled points.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
2. Curve Fitting
Curve fitting is an important type of interpolation in
many applications of. Curve fitting is divided into two
categories.
 2.1 exact interpolation : a fitted curve passes through all
given points.
 2.2 approximate interpolation : a fitted curve does not
always pass through all given points.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
2.1 Exact interpolation
There are three methods:
2.1(a) nearest neighbor : the same value as that
of the observation is given within the proximal
distance
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
2.1 Exact interpolation
2.1(b) linear interpolation: a piecewise
linear function is applied between two
adjacent points.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
2.1 Exact interpolation
• 2.1(c) cubic interpolation : a third order
polynomial is applied between two adjacent points
under the condition that the first and second order
differentials should be continuous.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
2.2. Approximate Interpolation
There are three methods;
2.2(a) Moving Average: a window with a range of -d to
+d is set to average the observation within the region
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
2.2 Approximate Interpolation
2.2(b) B-Spline: a cubic curve is
determined by using four adjacent
observations
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
2.2 Approximate Interpolation
2.2(c) Curve Fitting by Least Square Method.
Least square method (sometimes called regression model) is a
statistical approach to estimate an expected value or function with the
highest probability from the observations with random errors. The
highest probability is replaced by minimizing the sum of square of
residuals in the least square method.
Equation
Y  ax  b
Slope
a
 ( Xi  X )(Y  Y )
 ( Xi  X )
intercept
b  Y  aX
2
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
3. Interpolation by Surface Fitting
 the principle of surface fitting respectively to
interpolate the value at an unsampled point
using surrounding sampled points.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
3. Surface Fitting
• Surface fitting is widely used for interpolation of points on
continuous surfaces such as digital elevation model
(DEM), geoid, climate model (rainfall, temperature,
pressure etc.) and so on.
• Surface fitting is classified into two categories:
– 3.1 surface fitting for regular grid and
– 3.2 surface fitting for random points.
• 3.1 Surface Fitting for Regular Grid
Following two methods are commonly used.
3.1(a) Bilinear Interpolation
3.1(b) Bicubic Interpolation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
3.1 Surface Fitting for Regular Grid
3.1(a) Bilinear Interpolation
Bilinear function is used to interpolate z using the
following formula with respect to normalized
coordinates (u, v) of the original coordinates (x, y)
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
3.1Surface Fitting for Regular Grid
3.1(b) Bicubic Interpolation
Third order polynomial is used to fit a continuous
surface using 4 x 4 = 16 adjacent points.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
3.2 Surface Fitting for random
Points
3.2. (a) Triangular network called as Triangulated
Irregular Network (TIN) is applied
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Compare Interpolation methods
• Thiessen polygons are Used for service area analysis of public
facilities such as hospitals. Originally proposed to estimate aerial
averages precipitation in 1985.
• Inverse Distance Weighted can be a good way to take a first look
at an interpolated surface. However, there is no assessment of
prediction errors. Accuracy depends on the selection of a power
value and the neighborhood search strategy. A smaller (6) actually
produce better estimations than a larger number (12).
• Thin-plate Splines (applies to surface) are recommended for
smooth, continuous surfaces such as elevation and water table. Also
used for interpolating mean rainfall surface and land demand
surface.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Kriging
•
•
•
•
Kriging is a geostatistical method for spatial
interpolation.
It can assess the quality of prediction with estimated
prediction errors.
It uses statistical models that allow a variety of map
outputs including predictions, prediction standard
errors, probability, etc.
Semivariogram can be fitted as:
1. Ordinary Kriging models:
Spherical, Circular, Exponential,
Gaussian and Linear.
1. Universal Kriging models:
Linear with Linear drift, and
Linear with Quadratic drift
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Semivariogram
• The semivariogram functions
quantifies the assumption that
things nearby tend to be more
similar than things that are
farther apart. Semivariogram
measures the strength of
statistical correlation as a
function of distance.
• Semivariance:
Y(h) = ½ [(Z(xi) - Z(xj)]2
• Covarience = Sill – Y(h)
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Data Structure for Continuous
Surface Model
In GIS, continuous surface such as terrain surface, meteorological
observation (rain fall, temperature, pressure etc.) population
density and so on should be modeled
• Grid at regular intervals
– Bi-linear surface with four points or bi-cubic surface with
sixteen points is commonly used
• Random points
– Triangulated irregular network (TIN) is commonly used.
Interpolation by weighted polynomials is also used.
• Contour lines
– Interpolation based on proportional distance between
adjacent contours is used. TIN is also used.
• Profile
– Profiles are observed perpendicular to an alignment or a
curve such as high ways. In case the alignment is a straight
line, grid points will be interpolated. In case the alignment is
a curve, TIN will be generated.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Different Types of DEM
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Remote Sensing and GIS in Water Management © Dr. Saiful Islam, IWFM, BUET
DEM
• A DEM (digital elevation model) is digital
representation of topographic surface with the
elevation or ground height above any geodetic
datum. Followings are widely used DEM in GIS:
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
DTM

A DTM (digital terrain model) is digital representation of
terrain features including elevation, slope, aspect,
drainage and other terrain attributes.

Usually a DTM is derived from a DEM or elevation data.
several terrain features including the following DTMs.
1. Slope and Aspect
2. Drainage network
3. Catchment area
4. Shading
5. Shadow
6. Slope stability
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Examples of DTM
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
1. Slope and Aspect
(i) Slope
• The steepest slope (s) and the direction from the
east () can be computed from 3 x 3 matrix.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Slope calculation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Slope calculation
 Slope is defined by a plane tangent to a
topographic surface, as modelled by the
DEM at a point (Burrough, 1986).
 Slope is classified as a vector; as such it
has a quantity (gradient) and a direction
(aspect).
 Slope gradient is defined as the maximum
rate of change in altitude (tan )
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Example: Slope from elevation data
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
(ii) Aspect
• The aspect that is, the slope faced to azimuth is
180° opposite to the direction of q
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Figure 1. Slope components, note that slope gradient can be
express in percent or in degrees
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Aspect calculation
 Aspect identifies the steepest downslope
direction from each cell to its neighbors. It can
be thought of as slope direction or the compass
direction a hill faces.
 It is measured clockwise in degrees from 0 (due
north) to 360, (again due north, coming full
circle). The value of each cell in an aspect
dataset indicates the direction the cell's slope
faces. Flat areas having no downslope direction
are given a value of -1.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Example: aspect from the elevation
data
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
2. Drainage Network and
Watershed
• The lowest point out of the eight neighbors is
compared with the height of the central point
to determine the flow direction.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Surface Specific points
• + is assigned if the height of the central point is higher than
the one of the eight neighbors and - if lower.
– A peak can be detected if all the eight neighbors are lower.
– A pit or sink is formed if all the eight neighbors are higher
– A pass can be extracted if the + and - alternate around the central
point with at least two complete cycle.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Remote Sensing and GIS in Water Management © Dr. Saiful Islam, IWFM, BUET
4. Shade and 5.Shadow
• Shade is defined as reduced reflection depending on
the angle between the terrain surface and the incident
light such as the sun.
• Shadow is projected areas that the incident light cannot
reach because of visual hindrance of objects on terrain
relief
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Hill Shading
The effect of hill shading on the assumption of an ideally
diffused reflecting surface (called Lambertian surface)
can be computed as follows:
Relative shading = cos  = |nxsx + nysy+ nzsz |≤ 1.0
where  : angle between incident light vector s and surface normal n
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Altitude
• The altitude is the slope or angle of the
illumination source above the horizon. The
units are in degrees, from 0 (on the
horizon) to 90 degrees (overhead). The
default is 45 degrees.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Azimuth
• The azimuth is the angular direction of the
sun, measured from north in clockwise
degrees from 0 to 360. An azimuth of 90 is
east. The default is 315 (NW).
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Hillshading from elevation data
The hillshade
below has an
azimuth of 315
and an altitude
of 45 degrees.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Examples: A slope and hillshade
maps of Glacier National Park
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Using hill shading for display
• By placing an elevation raster on top of a created
hillshade, then making the elevation raster transparent,
you can create realistic images of the landscape.
Hillshade + elevation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Generation of Contour Lines
• Contour lines are one of the terrain features which
represent the relief of the terrain with the same
height. There are two types of contour lines in
visualizing GIS data:
• Vector Line Drawing
In case when the terrain points are given in grid, the
simplest method is to divide the square cell into two
triangles mechanically.
• Raster Image
Contour image with painted contour terraces, belts or
lines instead of vector lines will be generated in raster
form.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Interpolation of Elevation from
Contours
• Digital elevation model (DEM) is very often generated by
measuring terrain points along contour lines using a digitizer.
DEM with contour points should be provided with an algorithm
interpolate elevation at arbitrary points. There are several
interpolation methods as follows.
 Profile Method
A profile passing through the point to be interpolated will be
generated and linear or spline curve applied.
 Proportional Distance Method
According to distance to two adjacent contour lines, the
elevation is interpolated proportionally with respect to the
distance ratio.
 Window Method
A circular window is set up around a point to be interpolated and
adjacent terrain points are used to interpolate the value using
second order or third order polynomials.
 TIN Method
TINs are generated using terrain points along contour lines.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Interpolation Methods
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Examples: A Digital Elevation Model and
associated contour map of Glacier Nat'l
Park
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Automated Generation of DEM
• Automated generation of DEM is achieved by photogrammetric
methods based on stereo aerial photography and satellite stereo
imagery.
• Parallax is defined as difference between left and right photographs or
image coordinates. The higher the elevation is, the bigger the parallax
is. If the parallax is constant, equal elevation or contour lines will be
produced.
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Triangulated Irregular Network (TIN)
• Triangulated irregular network or TIN is a DEM with a
network of triangles at randomly located terrain points.
Contouring of TIN is based on
the following procedure:
step 1: find the intersect of contour and a
side.
step 2: assign the "reference point" with
the symbol r to the vertex above the contour
height and the "sub-point" with the symbol
s to the vertex below the contour height.
step 3: shift over to the transversing to find
the third vertex in the triangle by checking
whether it is a reference point (r) or subpoint (s).
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Example: TIN Creation
Remote Sensing and GIS in Water Management @ Dr. A.K.M. Saiful Islam
Thank you